## MATRIX - Count maximum matrices

You are given a matrix A of M rows and N columns, consisting of numbers 0 and 1. For a rectangle in A (sides >= 1), X1 is the number of ones on its sides, X0 is the number of zeros on its sides, and its *value* is defined as X1 – X0. Let us consider W, the maximum value taken over submatrices of A, and S, the number of submatrices with value W. Your task is to find W and S.

### Input

The first line of input contains the number of testcases t (t <= 15). The first line of each testcase contains the numbers M, N (1 <= M, N <= 200) Then M lines follow. In each line, there are N numbers 0 or 1.

### Output

For each testcase, you should output a single line with numbers W and S.

### Example

Input:1 5 6 1 1 1 1 1 1 1 0 0 0 0 1 1 0 0 0 0 1 1 0 0 0 0 1 1 1 1 1 1 1Output:18 1

Added by: | Lê Đôn Khuê |

Date: | 2005-06-08 |

Time limit: | 2.538s |

Source limit: | 50000B |

Memory limit: | 1536MB |

Cluster: | Cube (Intel G860) |

Languages: | All except: NODEJS PERL6 VB.NET |